{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.1.1Overlapping class distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "修改支持向量机，允许一些训练数据点被误分类。引入松弛变量$\\xi_n\\ge0$，每个训练数据点都有一个松弛变量。分类的限制条件为:\n",
    "$$t_ny(x_)\\ge1-\\xi_n$$\n",
    "+ $\\xi_n=0$的数据点被分类正确，在边缘上，或在边缘的正确一侧\n",
    "+ $0<\\xi_n\\leq1$的数据点位于边缘内部，但在决策边界的正确一侧、\n",
    "+ $\\xi_n>0$的数据点位于决策边界的错误一侧，是被错误分类的点。\n",
    "\n",
    "对比线性可分的情况，我们需要最小化$$C\\sum_{n=1}^N\\xi_n+\\frac{1}{2}\\lVert{w}\\lVert^2$$\n",
    "参数C类似于正则化系数\n",
    "Lagrange函数为:\n",
    "$$L(w,b,\\xi,a,\\mu)=\\frac{1}{2}\\lVert{w}\\lVert^2+C\\sum_{n=1}^N\\xi_n-\\sum_{n=1}^Na_n\\{t_ny(x_n)-1+\\xi_n\\}-\\sum_{n=1}^N\\mu_n\\xi_n$$\n",
    "其中${a_n\\ge0}$和${\\mu_n\\ge0}$是lagrange乘数，对应的KKT条件:\n",
    "$$\\begin{cases}\n",
    "a_n\\ge0\\\\\n",
    "t_ny(x_n)-1+\\xi_n\\ge0\\\\\n",
    "a_n(t_ny(x_n)-1+\\xi_n)=0\\\\\n",
    "\\mu_n\\ge0\\\\\n",
    "\\xi_n\\ge0\\\\\n",
    "\\mu_n\\xi_n=0\n",
    "\\end{cases}$$\n",
    "\n",
    "对$w,b,{\\xi_n}$进行最优化:\n",
    "$$\\frac{\\partial L}{\\partial w}=0\\Rightarrow w=\\sum_{n=1}^Na_nt_n\\phi(x_n)$$\n",
    "$$\\frac{\\partial b}{\\partial w}=0\\Rightarrow w=\\sum_{n=1}^Na_nt_n$$\n",
    "$$\\frac{\\partial \\xi}{\\partial w}=0\\Rightarrow a_n=C-\\mu_n$$\n",
    "\n",
    "得到对偶形式:\n",
    "$$\\tilde{L}(a)=\\sum_{n=1}^Na_n-\\frac{1}{2}\\sum_{n=1}^N\\sum_{m=1}^Na_na_mt_nt_mk(x_n,x_m)$$\n",
    "满足条件:\n",
    "$$\\begin{cases}\n",
    "0\\leq a_n\\leq C\\\\\n",
    "\\sum_{n=1}^Na_nt_n=0\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 对于数据点的一个子集，$a_n=0$，这些点对预测模型没有作用\n",
    "* $C\\ge a_n>0$的点组成了支持向量\n",
    "\n",
    "$C\\ge a_n>0$的支持向量满足$\\xi_n=0$即$y_ny(x_n)=1$,满足:\n",
    "$$t_n(\\mathop\\sum_{m\\in{s}}a_mt_mk(x_n,x_m)+b)=1$$\n",
    "$$b=\\frac{1}{N_M}\\mathop\\sum_{m\\in{s}}(t_n-\\mathop\\sum_{m\\in{s}}a_na_mt_mk(x_n,x_m))$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(r\"../\")\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.kernel import (\n",
    "    RBF,\n",
    "    PolynomialKernel,\n",
    "    SupportVectorClassifier,\n",
    "    RelevanceVectorRegressor,\n",
    "    RelevanceVectorClassifier\n",
    ")\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ihiRJry1GIlfKseP2DjxNeAobcxt0rNgRFZwq6J1DSQ5G1tH9LLhd0IsRFCWo2AIm/gKY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\nwa2YW3iwLxTKNBWmdJ+Da6HX4evSCo0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aQfj69etstfE5VFZDwqtTLk/O/KIc4unpyRs3\nbmisvayIgH46oCaxsbEoWlS9vHpf16+MhSdnIiEmAeOb/4pRjabh8qFAjFk5FF1GtEv3GpJ4/F8I\nAKBIpAVa3e2An/4KxpxrKQiLCQNJPH33DG5XBXQ/9h+2dN+CysUrQy6Xw2ekL66fuokfejWBZbkS\nmNrWA4+DngIAbGxsYGFhgeTkZLRr1w6ha0MR805R3srQuBAMJB8/AiaFjcX/GwgGYs0BQLE1uJhJ\nMUgMPj8d6l6zO8IqhMFnyc84dPQKRs8AUCpQnBowdgV23tqJtlXawriQ8WfbyohixYoBAPbu3Ysq\nVargxIkTal2XLEvGq9hXKhudPoXyWPDNYACFAKMmAAi+HQ9105dnh4CAALi4uODQoUNas/FZ1FUL\nTR75cSTQqlUrNm/ePEvXBF+6J37LrpuS/npzyO1Q3r58j2sn/862gh2Xj1zPI+tP0tbAnoM6/8Ih\n+4fSwtOCwiyBJRaW4NijY3k/6r54vc+o9eIUQC6XM/R+GPuUH85epZz59M5z8Ty5XM5Vq1ZRkAgs\nVaEU//3nijgFOLH5jDg1CL50jzfCb7DcknKZfuunx6PoRyy5sCRv3G3F6eMVwUQeHh6K6cybqQx/\n0pCVvSvxxMOMR0Tq8uzZM9atW5cSiYQrVqzIcFntTuQdDvtrGM3nm9NykSVN55qy3dZ2aaolKQqi\n2lMWXovyBEX/xKlB9EitOAZlMhmbNWvGUqVK8f37nFdiVgL9dEDzdOzYkVnpd+opQFvBTpwapEYu\nl3NcixnsaNZPFIC493Gc0NKNtgb2tJXYc9W4jSSZ4QN5ft9lbpyxXeUBCL0fxlm9vBj7VjXzjlQq\n5eJNiykpIqGRxJiNjH4UpwBKH0GXogNot9WOHmc91L7XT9l5cyetvEpxxeUl7DegHwFw9W+ruePm\ndlZd/hVnn52d7bY/JSYmhl27diUADho0iPHxqnsJTj8+TctFlvQ48yvDYxQhxgkpCfz9xu+suvwr\nup9xF8+Vy5MVYcIJqgIlj/1dZVqmSdavX08A3Lx5s0bb1YuAFnBxceGoUaPUOje1ABxcdZz3Ax+p\n+AhS8+pZJAdUGcmOZn0Z6P8fJ7R0YzuJPc/svMBLh64y5k3Wi08kxidy6LcTOLfPUrH2oFQqpeeA\n5RxUayy7r+5O0zKmrFrla5Ulz9CQF+y10IHfrPqGbxOyF22o5FLoJfbc1ZNF5hShaS1TQgC/Hfst\n/7r7V47aTQ+ZTMaZM2cSAPfu3UuSDH0Xyn+e/cOSC0vy1H8/URbV52PBErmcsvdL+DKkAb9eXpkH\n7x7UeJ/U4fnz5yxevPiH0GjNCoxeBHTMlWPXaGtgz4OrPm6HVQrB6vGb0pz/6lkk7Ut/9O6ru8Ho\nc+xadEDcuJSUmEzPAcvZVrDjtnl/MkWWwrH7x7KoS1H22mbHmX4zOerQKFp5WbHTtk588DR9z396\nxCTFcN/tfdx0fRNPPDyRJvPw24S3DHoWxO8afkcTExOeP6+9zTg3btzglhtb2GBtAxafVpyWiyxp\nONuQvbY3579BlUQhkL1fIuY63HFzO1ttbqW1Pn2OpKQkTp48mffv38/85CyiFwEtoq5ip56PKwm9\nHyZ+M6cmPiaeA6qMFEXgzr+a+VAohUB5bJunuill/5bDrN28MSs3rMJ6tvV4K+yWWL7syHr/z7ad\nmJLIiccnsviC4my3tR0d9zmyyfomLLekHFf8m3Z+HhkZyRo1arBYsWIMCtJ8ok65XM7RR0azzupa\nXHtiLU1NTVmycUluu7SNPpcXsNSiojxwqdwnyU5lTJImsahnUUbFaTcU/NO+ajsEWi8CWiAgIIDW\n1tYaX5+Oj4kXpwC7vQ7SseoodrVw1IgQSKVSFRH4VIAiX7ymU7XRrGlUjwDYoukP7FysHwdU/oXh\nTzJOlJIsTWb7P9rzx+WteOfZXZWfHbvox5pLa3H6ybSZcp88ecKyZcuybNmyGt8YtC1oG2uvrsk3\nz+owKcqN7u7uhAFYslQJ7vRtwEu32rGEpyHDHlX+ELMQI15baVklcbk1N5g9ezYrVqzIFy9eZH5y\nNtGLgBYIDw8nAHp7e2usTblczunt54g+AFIxNVAKwYuH2d8rr/QBtBXs2KPEQHFqkJ4QDKw+hrWg\nKBZqaWzNOzcyTv9NkmsC1rDFuhbsULgPRzWeJvotnt55TocyQ9m//s8sv6R8uoVMb968yWLFirFa\ntWqMiIjI9v19SpP1TXjgzgHK3i8UC440ml2PVWqYEQA72H7FQdvNOfdouQ/hy4qpwduEtzSfb873\niZrzzGeEXC6nh4cHAdDJySnTDFM5QS8CWqJ8+fJ0cHDQaJsBJ26k8QG8ehbJLbN2Z/tDkloAlFOA\n1D6CT4Xgn4NX2FawYx00o2EhQ/74448ZTnvkcjlrr65N/0f+/OfgFbY36s1Rjafx9uX7dCgzlHbW\nQxgS/Iye5z05+ED6iVcuXLhAU1NTfvfddxrZEPQy5iWLLShGqUz6wemnEIKNZ61pu86My+a35PQx\nxXn6liMbrWvEdxF7KQuvSVlUHy6/5EWHPZr9m6ZHQkIChw4dKgqANvagpEYvAlqif//+tLa2zvOl\nqJKTFKsTn/oAdi06wEmt3fn45lPxvbsBD9mtmBN/MuzNDsZ92MS0Nbf+tj3DtqPjo2k+31z8HSgF\npK1gxw4mfRkS/IykYm2+6vKqGbZz9OhRFipUiC1btkyzrJdVHkU/+iT/wWvKwqsxNrQqqy0zo8/Z\nDpS9/ZX/hd/gVxO+YtGiRekytTf9LrRgqUWWDHgRkCP76jB58mQC4IwZM3Ll85MVEdBHDGaBVq1a\n4dWrV7h582bmJ2eRewEPkRifpPLesY2nsXjIaoVaf+DFw3DMtl+MuHcZR70ZGhli1r4p6OeqWoHX\nfnJXJMUnY/pPc/H8fhjuXX2EabazIU2WAiC8zsxCzQrfYPeUo7j1z134+voiLCxMpQ0ZZTCUGIo1\nD8pXLyv+TFLIACXLlgAAGEuM05QmS02HDh2wZcsW/P3333BwcBCr8GYHq8JWiE6IRnRCNCiPBqMH\nATCCqYkNjna0gs+Nf9HtyA1sv7kDllaWaPy/xvD02oV2rS6g/tXvYBJtkm3bnyM2NhYhISEAAFdX\nRVr1uXPnZrkkmtZRVy3SOwDYAwgGIAfQUN3r8sNI4Onbp/S57MM55+Zw47WNfJvwluHh4Rw7diwf\nPlR/CU0d3kS8ZRfzAZxq68GEOEU8feSL1+z+YS7vM9qXcrmczx8oogF7WjqL37jpEXzxbpr37l19\nyOSkZD6++ZR2VoPpUHYYj204xS7mA9hWsOOBlcdEu8PqTOSRP06wSJEirFatGp8//7jSIZVJWXZJ\nWd58dVP0AdhZD+GOBfvFqUHMm1huur6Jnbd3zvTeV69eTQDs27dvjobIA/YN4KILHpRFdqEs/BvK\nE8+LU4P3z6ryt/OdxYhBm1U2HLFpBHsP6E0TExOWKlVKtB0Z+fm8jOoQGRnJ+fPn09ramt9//71O\nRo7IrekAgFoAagA4W1BEIDo+mva77VliYQkOOTiELv4u7LmrJ4stKEZXf9c0kXtSqVRl442Sa6eC\n0l0OzAi/LWdpa2DPqbYefPEwnINqjGHnIv05p89SthXs6NppHnuXG8aels4qG4Q+5e+9l9hWsONu\nr48BMIEn/2NH0778bZIiBdjjm09VNg7t8znCpISPOfyUD8Rp/9MsUqQIa9SowfDwj05K9zPu7Lej\nv4oPgORHH0Hzaaz/W/00YbkZ4enpSQAcPnx4th+YoJdBtFxUkmeDOqgkBpXL5ZS+W0D3E+1Zd01d\nJktVNwNFRUXx1ClFXoXHjx8TABs2bEhXV1ceOnQoS87Lw4cPs0OHDjQyMiIAtm3blpcuXcrW/eSU\nXBMBsZECIgIxSTH8bu137Lq4B0NCVL9pT506x4bLGtF5nzP//vtvMdHon96H0+wOPOrrn+ZBVAe/\nLWfFB7NdIQfe+ucu5XK5SvjxwxtPPtuGNEXK2Q5LRPtKARhWZyLfRCiiAJOTkun09SixzZndF3Jq\nu9mMe/9xbn54rR/7VvyZ+3cdpJmZGW1sbMQH4nX8a37t8zUdPPrx0S3V/pw5cJ6tl7Rlhz86UCZX\n37Hp4uJCAJwwYUK2heDko5O0XGTJ/n/25/EHx3n1xVVu/W8rv/f9nnXX1M20BPrLly85d+5cNmvW\njBKJhAAIgH/9pYhyvHTpEp2cnDho0CA6OjqyU6dOrF+/vvhZ8Pb2ZpUqVThx4kTeunUrW/egKfKk\nCAAYDuAqgKsVK1bU9u8gWyw4v4Bdfu/Czub9OajGGEaFKfa737xwh13MB3Bww7GsOLsiDQwMOGPG\nDJIfQoRTFfBQCoBLh7kq365KQu+9YORz1cCU+NgE3r58n5EvXosPZufC/ZkQlyhOAZTvrxyzIdOH\nJLUQtBXs0giAW7cFbCvY0XvEWtpZDVaMCgzs2LlIf754GM7Da/3YVrDjpB9nclD1MVy3ZAPNzMy4\nfftHh2Hou1B+v+F7VvauTPcz7lx9ZTXHHxsvPoRxyerVZVAil8s5duxYAqCbm1uWrk3N6/jXXHJx\nCVtsbMF6v9Vj5+2d+eftP9NEMmZGbGwsz549y6VLl4rToX379rFSpUqsUKECv/rqK9avX58dO3YU\ng59SUlLyjNNYoyIAwB/ArXSObsyCCKQ+8uJIQCaX8SvvrxjwIoA3z99mF/MBHFRjDM/tucgu5gM4\nsPoYRr54zWWXlrFsg7IsU6YMU1IUH6zUQvA5AZBKpXSuOZZO1UaLQhAfm8DJrd3ZuUh/OlYdyS7m\nA+g9Yi1tDew5trmrOAV4eOMJ10zYpLYQXDl2TezP+mlbSSo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AMvmouhmItU2D9g1oYGjA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\nhfN/aZy9For92i0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcfe6f3eda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def create_toy_data():\n",
    "    x0 = np.random.normal(size=100).reshape(-1, 2) - 1.\n",
    "    x1 = np.random.normal(size=100).reshape(-1, 2) + 1.\n",
    "    x = np.concatenate([x0, x1])\n",
    "    y = np.concatenate([-np.ones(50), np.ones(50)]).astype(np.int)\n",
    "    return x, y\n",
    "\n",
    "x_train, y_train = create_toy_data()\n",
    "\n",
    "model = SupportVectorClassifier(RBF(np.array([1., 0.5, 0.5])), C=1.)\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "x0, x1 = np.meshgrid(np.linspace(-4, 4, 100), np.linspace(-4, 4, 100))\n",
    "x = np.array([x0, x1]).reshape(2, -1).T\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], s=40, c=y_train, marker=\"x\")\n",
    "plt.scatter(model.X[:, 0], model.X[:, 1], s=100, facecolor=\"none\", edgecolor=\"g\")\n",
    "plt.contour(x0, x1, model.distance(x).reshape(100, 100), np.arange(-1, 2), colors=\"k\", linestyles=(\"dashed\", \"solid\", \"dashed\"))\n",
    "plt.xlim(-4, 4)\n",
    "plt.ylim(-4, 4)\n",
    "plt.gca().set_aspect(\"equal\", adjustable=\"box\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "核函数对应于特征空间中的内积。特征空间可以是⾼维的，甚⾄是⽆穷维的。\n",
    "通过直接对核函数操作，⽽不显式地引⼊特征空间，⽀持向量机或许在⼀定程度上避免了维度\n",
    "灾难的问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.1.2与Logistic回归的关系\n",
    "\n",
    "对于分类正确的点,满足$y_nt_n\\ge1$,有$\\xi_n=0$,剩下的点有$\\xi_n=1-y_nt_n$,目标函数keloid写成\n",
    "$$\\sum_{n=1}^NE_{SV}(y_nt_n)+\\lambda\\lVert{w}\\lVert^2$$\n",
    "其中$\\lambda=(2C)^{-1}$，$E_{SV}$是hinge误差函数:\n",
    "$$E_{SV}(y_nt_n)=[1-y_nt_n]_{+}$$\n",
    "而$$\\sum_{n=1}^NE_{LR}(y_nt_n)+\\lambda\\lVert{w}\\lVert^2$$\n",
    "$$E_{LR}(yt)=ln(1+exp(-yt))$$\n",
    "关键的区别在\n",
    "于$E_{SV} (yt)$的平台区域产⽣了稀疏解,最小化分类错误率时，一个单调递减的误差函数是更好的选择"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f248d32c748>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iqUhRqOYa7Erud7nkfZ9HVWH9d2M75ZbqzqlLTpzAKp1ThRDNhBSFaq5BrvgN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\nuQAAAAhJREFUpjX7fw9sqJmKRZiuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f24913bd0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(-2,3,1001,dtype=np.float)\n",
    "y_logit=np.log(1+np.exp(-x))/np.log(2)\n",
    "y_boost=np.exp(-x)\n",
    "y_0_1=x<0\n",
    "y_hinge=1.0-x\n",
    "y_hinge[y_hinge<0]=0\n",
    "y_square=(x-1)**2\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot(x,y_logit,'r',label='Logistic Loss',lw=2)\n",
    "plt.plot(x,y_0_1,'g',label='0/1 Loss',lw=2)\n",
    "plt.plot(x,y_hinge,'b',label='Hinge Loss',lw=2)\n",
    "plt.plot(x,y_boost,'m--',label='Adaboost Loss',lw=2)\n",
    "plt.plot(x,y_square,'c-.',label='Square Loss',lw=2)\n",
    "plt.grid()\n",
    "plt.ylabel(\"$E_(z)$\",fontsize=16)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
